Reasoning requirements in school mathematics textbooks: an analysis of books from 12 countries
(English)Manuscript (preprint) (Other academic)
A selection of secondary school textbooks from twelve countries in five continents is used as an indicator of the opportunities to learn mathematics through different forms of reasoning, in particular with respect to the distinction between rote learning and deeper learning. One aspect that is fundamental to the development of conceptual understanding as well as problem solving ability is the opportunity to learn how to construct mathematically well-founded reasoning. This study compared textbook tasks to the information provided previously in the book, determining if it is possible and reasonable to mimic available solution templates, or if a solution has to be constructed. The results show that the percentage of tasks where it is possible to mimic available templates is on average 79 %, but that this percentage varies widely within the books depending on the textbook authors own labeling of the tasks, and on the mathematical content. 13 % of the tasks can be solved mainly by mimicking provided templates but require some minor modification, and the remaining 9 % of the tasks require that the main parts of the solution are constructed without the guidance of a template. Although these distributions are relatively similar in all textbooks, the twelve countries perform differently in international tests such TIMSS and PISA.
Mathematics Textbooks, Mathematics Tasks, Mathematical reasoning, Opportunities to learn, Secondary school
IdentifiersURN: urn:nbn:se:liu:diva-117560OAI: oai:DiVA.org:liu-117560DiVA: diva2:810726